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question:Find 2.4 times X. If we know the answer to the above question is 0.48, what is the value of unknown variable X?
answer:We want to find the value of X in the given situation. We are given the equation: 2.4 times X = 0.48 To solve for X, we can divide both sides of the equation by 2.4: frac{2.4 times X}{2.4} = frac{0.48}{2.4} Simplifying, we have: X = 0.2 The value of X is 0.2. The answer is: 0.2
question:f Javier spends 30 minutes outlining his speech, 28 more minutes writing than outlining, and half as much time practicing as writing, what is the total amount of time he spends on his speech?
answer:Javier spends 30 minutes outlining his speech. He spends 28 more minutes writing than outlining, so he spends 30 + 28 = 58 minutes writing. He spends half as much time practicing as writing, so he spends 58 / 2 = 29 minutes practicing. The total amount of time he spends on his speech is 30 + 58 + 29 = 117 minutes. 117 The answer is: 117
question:f Johnny purchases 15 packs of colored pencils for his class, with each pack containing a red, yellow, and green pencil, and he discovers that 3 of the packs have two extra red pencils, what is the total number of red colored pencils that Johnny bought?
answer:Each pack of colored pencils contains 1 red pencil. So, Johnny bought 15 packs x 1 red pencil = 15 red pencils in total. However, 3 of the packs have 2 extra red pencils, so there are 3 packs x 2 extra red pencils = 6 extra red pencils. Therefore, the total number of red colored pencils that Johnny bought is 15 + 6 = 21. 21 The answer is: 21
question:As n ranges over the positive integers, what is the sum of all possible values of the greatest common divisor of 3n+4 and n?
answer:Let gcd(3n+4,n)=d. Then d divides both 3n+4 and n. Since d divides n, it also divides 3n, and therefore it divides (3n+4) - 3n = 4. Thus, the possible values of d are the positive divisors of 4, which are 1, 2, and 4. To find the sum of all possible values of d, we sum these three values: 1+2+4=boxed{7}. The answer is: 7